Resonant machine learning uses electrical network dynamics to optimize learning efficiently.
problem Traditional energy-based learning models are dissipative and inefficient.
method Proposes a new learning framework with two energy components (active and reactive) to ensure active-power dissipation during learning.
result Support vectors in resonant SVMs correspond to self-sustained oscillations in an LC network.
A machine learning framework predicts self-induced stochastic resonance in neurons.
problem Predicting coherent oscillations in slow-fast excitable systems driven by noise.
method Physics-informed machine learning with a Noise-Augmented State Predictor architecture and Kramers' escape theory constraints.
result Trained PINN accurately predicts spike-train coherence on noise intensity, excitability, and timescale separation.
Two methods use simulation to improve anomaly detection in particle physics.
problem Artificial bumps in invariant mass spectra from machine learning classifiers.
method Simulation-assisted decorrelation techniques.
result Both methods are robust to correlations in the data and improve anomaly detection.
Bayesian neural network predicts planetary instability.
problem Predicting planetary instability in compact systems.
method Novel Bayesian neural network trained on raw orbital elements.
result Model predicts planetary instability times with high accuracy and robust generalization.
Due to the rapid innovation of technology and the desire to find and employ biomarkers for neurodegenerative disease, high-dimensional data classification problems are routinely encountered in neuroimaging studies. To avoid over-fitting and to explore relationships between disease and potential biomarkers, feature lear…
This study assesses the reproducibility of 1H-MRS scans across different vendors and sessions.
problem Lack of harmonization in magnetic resonance spectroscopy protocols among vendors.
method Analysis of CV and ICC for within- and between-sessions, and correlation coefficients for across machines.
result Metabolite concentrations are highly reproducible across different vendors and sessions.
Independent component analysis (ICA), as an approach to the blind source-separation (BSS) problem, has become the de-facto standard in many medical imaging settings. Despite successes and a large ongoing research effort, the limitation of ICA to square linear transformations have not been overcome, so that general INFO…
QC methods improve reliability of machine learning-based image segmentation.
problem Inaccuracies in machine learning algorithms limit their clinical applicability.
method Analysis and validation of QC approaches for automatic segmentation.
result Aggregation of uncertainty and Dice prediction methods improved segmentation reliability.
This survey samples from the ever-growing family of adaptive resonance theory (ART) neural network models used to perform the three primary machine learning modalities, namely, unsupervised, supervised and reinforcement learning. It comprises a representative list from classic to modern ART models, thereby painting a g…
Machine learning techniques have gained prominence for the analysis of resting-state functional Magnetic Resonance Imaging (rs-fMRI) data. Here, we present an overview of various unsupervised and supervised machine learning applications to rs-fMRI. We present a methodical taxonomy of machine learning methods in resting…
Develops statistical guarantees for image-to-image regression models.
problem Current image-to-image regression models lack statistical guarantees for model mistakes and hallucinations.
method Uncertainty quantification techniques with rigorous statistical guarantees for image-to-image regression problems.
result Derives uncertainty intervals around each pixel with formal mathematical guarantees.
We implement machine learning algorithms to nuclear data. These algorithms are purely data driven and generate models that are capable to capture intricate trends. Gradient boosted trees algorithm is employed to generate a trained model from existing nuclear data, which is used for prediction for data of damping parame…
Holomorphic vector bundles on Hopf manifolds admit flat connections.
problem Understanding flat connections on holomorphic vector bundles over Hopf manifolds.
method Defining resonant and non-resonant Mall bundles, proving the existence of flat connections on non-resonant bundles, and applying the Poincare-Dulac theorem.
result Non-resonant Hopf manifolds are linearizable, generalizing Kodaira's result.
SGDm with fixed step-size diverges under covariate shift, similar to a parametric oscillator.
problem SGDm with fixed step-size diverges under covariate shift.
method Approximated learning system as a time-varying system of ODEs and characterized divergence/convergence modes.
result SGDm with fixed step-size can diverge under covariate shift, similar to resonance in oscillators.
New resonance theory for Anosov flows connects spectral properties to mixing measures.
problem Defining and analyzing Ruelle-Taylor resonances for Anosov actions.
method Combining microlocal methods and J. Taylor's cohomological theory, defining Ruelle-Taylor resonances and proving Fredholm theory.
result Ruelle-Taylor resonances form a discrete subset of Cκ with λ=0 being a leading resonance. We study the distribution of resonances for geometrically finite hyperbolic surfaces of infinite area by countting resonances numerically. The resonances are computed as zeros of the Selberg zeta function, using an algorithm for computation of the zeta function for Schottky groups. Our particular focus is on three aspe…
Accelerating Magnetic Resonance Imaging (MRI) by taking fewer measurements has the potential to reduce medical costs, minimize stress to patients and make MRI possible in applications where it is currently prohibitively slow or expensive. We introduce the fastMRI dataset, a large-scale collection of both raw MR measure…
Study reveals a link between Ruelle-Pollicott resonances and cohomology eigenvalues for Anosov diffeomorphisms.
problem Understanding the speed of mixing in Anosov diffeomorphisms.
method Investigates Ruelle-Pollicott resonances on manifolds of any dimension, connecting them to cohomology eigenvalues of a quasi-compact transfer operator.
result Established a cohomological bound for the speed of mixing of Anosov diffeomorphisms.
For compact and for convex co-compact oriented hyperbolic surfaces, we prove an explicit correspondence between classical Ruelle resonant states and quantum resonant states, except at negative integers where the correspondence involves holomorphic sections of line bundles.
Study compares ML and DL methods for autism classification.
problem Classifying autism from healthy individuals using rs-fMRI data.
method Developed classification frameworks for rs-fMRI connectivity patterns.
result Best model achieved 71% accuracy on multisite ABIDE I data.
Applications of machine learning tools to problems of physical interest are often criticized for producing sensitivity at the expense of transparency. To address this concern, we explore a data planing procedure for identifying combinations of variables -- aided by physical intuition -- that can discriminate signal fro…
We develop theoretical foundations of Resonator Networks, a new type of recurrent neural network introduced in Frady et al. (2020) to solve a high-dimensional vector factorization problem arising in Vector Symbolic Architectures. Given a composite vector formed by the Hadamard product between a discrete set of high-dim…
We discuss inverse resonance scattering for the Laplacian on a rotationally symmetric manifold M=(0,∞)×Y whose rotation radius is constant outside some compact interval. The Laplacian on M is unitarily equivalent to a direct sum of one-dimensional Schrödinger operators with compactly supported potenti…
Survey of deep learning methods for fMRI natural image reconstruction.
problem Reconstructing natural images from fMRI brain activity.
method Survey of deep learning approaches, including architectural design, datasets, and evaluation metrics.
result Performance evaluation across standardized metrics.
The study finds resonance points in polarised curves with polynomial conserved quantities.
problem Finding resonance points in polarised curves with polynomial conserved quantities.
method Using the non-orthogonality assumption on the conserved quantity, the study deduces the existence of resonance points.
result Every finite type polarised curve in the conformal 2-sphere with a polynomial conserved quantity admits a resonance point.
Study of spectral properties of Lorentzian quasi-Fuchsian manifolds.
problem Understanding the spectral properties of Lorentzian quasi-Fuchsian manifolds.
method Analyzing the geodesic flow, Ruelle resonances, and pseudo-Riemannian Laplacian.
result Meromorphic extension of the resolvent of the pseudo-Riemannian Laplacian with poles of finite rank.
The resonant band is a useful notion for the computation of the nontrivial monodromy eigenspaces of the Milnor fiber of a real line arrangement. In this article, we develop the resonant band description for the cohomology of the Aomoto complex. As an application, we prove that real 4-nets do not exist.
We show that the resolvent of the Laplacian on SL(3,R)/SO(3) can be lifted to a meromorphic function on a Riemann surface which is a branched covering of C. The poles of this function are called the resonances of the Laplacian. We determine all resonances and show that the corresponding residue op…
We find a resonance free region polynomially close to the critical line on Conformally compact manifolds with polyhomogeneous metric.
Uniform spectral gap for convex cocompact hyperbolic surfaces and expanders.
problem Spectral gap for convex cocompact hyperbolic surfaces and their covers.
method Using thermodynamic formalism for twisted Selberg zeta functions.
result Uniform resonance-free regions for convex cocompact hyperbolic surfaces and expanders.
Algorithm integrates uncertainty for lifelong learning in dynamic environments.
problem Continuous, lifelong learning for intelligent agents in changing conditions.
method Inspired by neuromodulatory mechanisms, integrates uncertainty for self-supervised and one-shot learning.
result Stable learning without catastrophic forgetting in a virtual environment.
New Bayesian method for joint sparse parameter inference.
problem Inference of jointly sparse parameter vectors from multiple measurements.
method Hierarchical Bayesian learning with joint sparsity-promoting priors.
result New algorithms consistently outperform existing methods in numerical experiments.
A machine learning method predicts rock permeability from 3D images.
problem Efficiently predict permeability of heterogeneous rocks for planetary and robotic applications.
method Machine learning guided 3D properties recognition of rock morphology from 3D micro CT and MRI images.
result The morphology decoder method accurately predicts permeability from 3D images.
Deep learning improves automated detection of epileptic seizures.
problem Automated detection of epileptic seizures using traditional methods is limited.
method Deep learning techniques for feature extraction and classification.
result Deep learning enhances accuracy in diagnosing epileptic seizures.
iCVI-ARTMAP accelerates clustering with adaptive resonance theory and validity indices.
problem Improving clustering efficiency and accuracy using adaptive resonance theory.
method Integrates adaptive resonance theory (ARTMAP) with incremental cluster validity indices (iCVIs) for clustering.
result Significantly reduces clustering time and outperforms other methods on synthetic and real-world data.
We investigate the resonance varieties, lower central series ranks, and Chen ranks of the pure virtual braid groups and their upper-triangular subgroups. As an application, we give a complete answer to the 1-formality question for this class of groups. In the process, we explore various connections between the Alexande…
New technique halves scan time for multi-echo MR images.
problem Slow acquisition of multi-echo magnetic resonance images.
method Structured deep dictionary learning for adaptive reconstruction.
result Scan time reduced by half compared to state-of-the-art.
Designs chiral photonic structures using machine learning for efficient optical properties.
problem Optimizing chiral photonic nanostructures for light-matter interactions.
method Evolutionary algorithm and neural network approach for rapid optimization.
result Frequency-dependent modification in reflected light's degree of circular polarization.
For a conformally compact manifold that is hyperbolic near infinity and of dimension n+1, we complete the proof of the optimal O(rn+1) upper bound on the resonance counting function, correcting a mistake in the existing literature. In the case of a compactly supported perturbation of a hyperbolic manifold, we es…
Paper proposes a faster neural machine translation model using election methods and Q-learning.
problem Slower inference time in complex attention models.
method Modelled attention network using election methods and Q-learning.
result Inference time is less than a standard Bahdanau translator, results comparable.
Study resonant forms for dissipative Anosov flows on 3-manifolds.
problem Determine resonant forms and their cohomology classes for dissipative Anosov flows.
method General theory including horocyclic invariance and local geometry analysis.
result Explicit computation of resonant forms and helicity for quasi-Fuchsian flows.
Deep neural networks correct Mie scattering in FTIR spectra of biological samples.
problem Mie scattering obscures biochemically relevant spectral information in FTIR spectra of biological samples.
method Deep neural networks to approximate the preprocessing function that removes Mie scattering.
result The model is faster and more generalizable across different tissue types.
The isoresidual fibration maps Riemann sphere strata to resonance arrangements.
problem Mapping Riemann sphere strata to resonance arrangements.
method Defining isoresidual fibration and studying its properties using tree structures.
result The isoresidual fibration is an unramified cover of degree a!/(a+2-p)! above the complement of a hyperplane arrangement.
Study geometric structures on LVM threefolds, focusing on resonant structures.
problem Understanding deformations of geometric structures on LVM threefolds.
method Using the Ehresmann-Thurston principle and Kuranishi family construction.
result Construction of a family containing all LVM threefolds and complete at every point.
Study of resonances and residue operators for hyperbolic spaces.
problem Understanding resonances and residue operators for pseudo-Riemannian hyperbolic spaces.
method Analyzing the resolvent of the Laplace-Beltrami operator on pseudo-Riemannian hyperbolic spaces.
result Explicit determination of resonances and identification of residue representations.
Machine learning for ASD diagnosis using morphological MRI networks.
problem Challenging to diagnose ASD using MRI due to heterogeneity and incomplete network neuroscience.
method Crowdsourced Kaggle competition to develop and benchmark ML pipelines.
result First-ranked team achieved 70% accuracy, 72.5% sensitivity, and 67.5% specificity.
SrvfNet aligns multiple functional data to templates without supervision.
problem Aligning large collections of functional data to templates without labeled data.
method Generative deep learning framework using SRVF and fully-connected layers.
result Framework achieves alignment and optimal template prediction without supervision.
We study the spectral theory of asymptotically hyperbolic manifolds with ends of warped product type. Our main result is an upper bound on the resonance counting function with a geometric constant expressed in terms of the respective Weyl constants for the core of the manifold and the base manifold defining the ends.